@AlexShura Email response (below) does not contain the polynomial in a(n). Please advise how you got that.

Greetings from The On-Line Encyclopedia of Integer Sequences! https://oeis.org/

> lookup 1 2 4 5 8 12 14 16 28 32 37 64 94 106 128 144 232 256 289 320

> 512 560 704 760 838 1024 1328 1536 1944 2048 2329 3104 3328 4096 4864

> 6266 6802 7168 8192 11952 15360 16384 16428 19149 28928 32768

a(n) = 1, 2, 4, 5, 8, 12, 14, 16, 28, 32, 37, 64, 94, 106, 128, 144, 232, 256, 289, 320, 512, 560, 704, 760, 838, 1024, 1328, 1536, 1944, 2048, 2329, 3104, 3328, 4096, 4864, 6266, 6802

# Direct matches

These sequences match the query directly.

oeis.org/search?q=1,2,4,5,8,12,14,16,28,32,37,64,94,106,128,144,232,256,289,320,512,560,704,760,838,1024,1328,1536,1944,2048,2329,3104,3328,4096,4864,6266,6802

oeis.org/A035001 Sorted elements of table (A035002) of a(m,n) =

sum(a(m-k,n), k=1..m-1)+sum(a(m,n-k), k=1..n-1).

<1, 2, 4, 5, 8, 12, 14, 16, 28, 32, 37, 64, 94, 106, 128, 144, 232,

256, 289, 320, 512, 560, 704, 760, 838, 1024, 1328, 1536, 1944, 2048,

2329, 3104, 3328, 4096, 4864, 6266, 6802>, 7168, 8192, 11952, 15360,

16384, 16428, 19149, 28928, 32768, 37120, 42168

# Transformations

These sequences match transformations of the original query.

T001 a(n) itself

= 1, 2, 4, 5, 8, 12, 14, 16, 28, 32, 37, 64, 94, 106, 128, 144, 232, 256, 289, 320, 512, 560, 704, 760, 838, 1024, 1328, 1536, 1944, 2048, 2329, 3104, 3328, 4096, 4864, 6266, 6802

oeis.org/A035001 Sorted elements of table (A035002) of a(m,n) =

sum(a(m-k,n), k=1..m-1)+sum(a(m,n-k), k=1..n-1).

<1, 2, 4, 5, 8, 12, 14, 16, 28, 32, 37, 64, 94, 106, 128, 144, 232,

256, 289, 320, 512, 560, 704, 760, 838, 1024, 1328, 1536, 1944, 2048,

2329, 3104, 3328, 4096, 4864, 6266, 6802>, 7168, 8192, 11952, 15360,

16384, 16428, 19149, 28928, 32768, 37120, 42168

# Transformations as Deltas

The deltas of these sequences match transformations of the original query.

T018 a(n+1) - a(n)

= 1, 2, 1, 3, 4, 2, 2, 12, 4, 5, 27, 30, 12, 22, 16, 88, 24, 33, 31, 192, 48, 144, 56, 78, 186, 304, 208, 408, 104, 281, 775, 224, 768, 768, 1402, 536 (as deltas)

oeis.org/A035001 Sorted elements of table (A035002) of a(m,n) =

sum(a(m-k,n), k=1..m-1)+sum(a(m,n-k), k=1..n-1).

<1, 2, 4, 5, 8, 12, 14, 16, 28, 32, 37, 64, 94, 106, 128, 144, 232,

256, 289, 320, 512, 560, 704, 760, 838, 1024, 1328, 1536, 1944, 2048,

2329, 3104, 3328, 4096, 4864, 6266, 6802>, 7168, 8192, 11952, 15360,

16384, 16428, 19149, 28928, 32768, 37120, 42168

In transformation descriptions,

Sn(z) denotes the ordinary generating function with coefficients a(n), and

En(z) denotes the exponential generating function with coefficients a(n).

___________________________________________________________________________

o You can look up sequences online at the OEIS web site https://oeis.org/ o For an explanation of the format used in the OEIS,

see https://oeis.org/wiki/Style_Sheet o If your sequence was not in the OEIS and is of general interest,

please submit it using the submission form https://oeis.org/Submit.html o The email address <sequences@oeis.org> does a simple lookup in the

On-Line Encyclopedia of Integer Sequences, a limited form of the search

available on the web site.

o If you send an empty message, you will be sent the help file.

Sequentially yours,

The On-Line Encyclopedia of Integer Sequences.

Maintained by The OEIS Foundation Inc., https://oeisf.org.

Please donate!

P.S. This content is made available under the terms of The OEIS End-User License Agreement: https://oeis.org/LICENSE